Biomolecules undergo cooperative folding transitions. Analytical theory has been available to provide a detailed understanding only for the helix/coil transition. We developed a new theory for a broad class of sequence-dependent transitions among secondary structures in RNA molecules and beta-hairpins in proteins. The theory predicts the stable states of 5 different RNA molecules and their denaturation thermodynamics. RNAs are predicted to have a rich variety of behaviors, including 1-state and 2- state transitions and "on-pathway" and "off-pathway" intermediate states, depending on the nucleotide sequence and solvent conditions. Compared to proteins, RNA folding landscapes may be quite rugged. The Computer Graphics Laboratory provides very useful facilities to display the RNA structures. The display of the actual molecular structure helps us to better understand the sequence-structure relationships.